The invention relates to a fuel injection pump for use in internal combustion engines, including a fuel distributor driven in rotation at a speed synchronous with the engine speed. The pump further includes a valve slide surrounding the fuel distribution member and displaceable axially by a hyraulic control mechanism. Control edges, surfaces and recesses internal to the valve slide cooperate with radial bores in the fuel distribution member of the pump for controlling the overall injected fuel quantity. The pump is supplied with fuel by a fuel supply pump which is driven at a speed proportional to the engine rpm. In a known fuel injection system of this type, for example as described in U.S. Pat. No. 2,828,727, the possibilities for adaptation to the present day requirements made of engine manufacturers are very limited. In addition, the hydraulic regulator is separate from the actual injection pump.